Not knowing all of the answers to all of the questions that I would ask you face to face, I would most likely start by regressing your upper body resistance training program. And I would really only do this to an extreme if the imbalance was causing discomfort and/or dysfunction. The weaker arm would dictate the load and rep range for both sides in all exercises.
Yes, this would slow down progress for the strong side. But that is the point. It may be that this would never resolve completely. That is possible, even likely. But in the case of dysfunctional imbalance, not proceeding accordingly will result in continued dysfunction and eventual injury.